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Process of repeating items in a self-similar way
Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines
Recursion
Topics referred to by the same term
Look up recursion in Wiktionary, the free dictionary. Recursion is the process of repeating items in a self-similar way. Recursion may also refer to Recursion
Recursion_(disambiguation)
Use of functions that call themselves
recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves
Recursion_(computer_science)
2019 novel by Blake Crouch
Recursion is a thriller science fiction novel by American writer Blake Crouch, first published in the United States in June 2019 by the Crown Publishing
Recursion_(Crouch_novel)
Topics referred to by the same term
Recursion theorem can refer to: The recursion theorem in set theory Kleene's recursion theorem, also called the fixed point theorem, in computability theory
Recursion_theorem
The Panjer recursion is an algorithm to compute the probability distribution approximation of a compound random variable S = ∑ i = 1 N X i {\displaystyle
Panjer_recursion
Two functions defined from each other
In mathematics and computer science, mutual recursion is a form of recursion where two or more mathematical or computational objects, such as functions
Mutual_recursion
Subroutine call performed as final action of a procedure
tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end recursion) is particularly useful, and is often easy to optimize
Tail_call
Theory of computer sciences
In the formal language theory of computer science, left recursion is a special case of recursion where a string is recognized as part of a language by the
Left_recursion
Recursive algorighm in linear algebra
Levinson recursion or Levinson–Durbin recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz
Levinson_recursion
Repetition of a process
and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. In mathematics, iteration may refer
Iteration
Theorem in computability theory
In computability theory, Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions
Kleene's_recursion_theorem
In computer programming, Walther recursion (named after Christoph Walther) is a method of analysing recursive functions that can determine if the function
Walther_recursion
In mathematics, topological recursion is a recursive definition of invariants of spectral curves. It has applications in enumerative geometry, random
Topological_recursion
American author (born 1978)
15, 1978) is an American author known for books such as Dark Matter, Recursion, Upgrade, and his Wayward Pines Trilogy, which was adapted into a television
Blake_Crouch
Set of recursion relations in quantum field theory
The Britto–Cachazo–Feng–Witten recursion relations are a set of on-shell recursion relations in quantum field theory. They are named for their creators
BCFW_recursion
programming formalisms — such as restricted formal languages, type systems, or recursion schemes — whose expressive power coincides exactly with a given complexity
Implicit computational complexity
Implicit_computational_complexity
Programming paradigm based on applying and composing functions
depth of recursion. This could make recursion prohibitively expensive to use instead of imperative loops. However, a special form of recursion known as
Functional_programming
Mathematical theorem
In mathematics, the transfinite recursion theorem says a function can be defined using a recursion over a well-ordered set; for example, N {\displaystyle
Transfinite_recursion_theorem
In computer science, polymorphic recursion (also referred to as Milner–Mycroft typability or the Milner–Mycroft calculus) refers to a recursive parametrically
Polymorphic_recursion
Subfield of mathematics
mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical
Mathematical_logic
Study of computable functions and Turing degrees
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated
Computability_theory
Concept in mathematical logic
type theory (ITT), a discipline within mathematical logic, induction-recursion is a feature for simultaneously declaring a type and function on that
Induction-recursion
Algorithms which recursively solve subproblems
they use tail recursion, they can be converted into simple loops. Under this broad definition, however, every algorithm that uses recursion or loops could
Divide-and-conquer_algorithm
Type of binary relation
and recursion on S gives primitive recursion. If we consider the order relation (N, <), we obtain complete induction, and course-of-values recursion. The
Well-founded_relation
Theoretical framework in linguistics
Minimal recursion semantics (MRS) is a framework for computational semantics. It can be implemented in typed feature structure formalisms such as head-driven
Minimal_recursion_semantics
In recursive function theory, double recursion is an extension of primitive recursion which allows the definition of non-primitive recursive functions
Double_recursion
Web browser developed by Google
performed poorly on recursion-intensive benchmarks, such as those of Google, because the Mozilla team had not implemented recursion-tracing yet. Two weeks
Google_Chrome
Algorithm to search the nodes of a graph
Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and
Breadth-first_search
In programming languages, the object or class the currently running code belongs to
recursion, and means that these methods can be overridden by derived classes or objects. By contrast, direct named recursion or anonymous recursion of
This_(computer_programming)
Type of software bug
allowing infinite recursion of a specific sort—tail recursion—to occur without stack overflow. This works because tail-recursion calls do not take up
Stack_overflow
Extension of recursion theory to admissible ordinals beyond the natural numbers
In recursion theory, α recursion theory is a generalisation of recursion theory to subsets of admissible ordinals α {\displaystyle \alpha } . An admissible
Alpha_recursion_theory
Pattern defining an infinite sequence of numbers
(analysis of algorithms) Mathematical induction Orthogonal polynomials Recursion Recursion (computer science) Time scale calculus Jacobson, Nathan, Basic Algebra
Recurrence_relation
Mathematical concept
chosen. More formally, we can state the Transfinite Recursion Theorem as follows: Transfinite Recursion Theorem (version 1). Given a class function G: V
Transfinite_induction
Higher-order function Y for which Y f = f (Y f)
or a for loop. Used in this way, the Y combinator implements general recursion. The lambda calculus does not have global names, for a function to refer
Fixed-point_combinator
Generalized form of recursion
Bar recursion is a generalized form of recursion developed by C. Spector in his 1962 paper. It is related to bar induction in the same fashion that primitive
Bar_recursion
Motorcycle model introduced in 2013
The Suzuki Recursion is a turbocharged concept motorcycle shown by Suzuki at the 2013 Tokyo Auto Show. The engine is a 588 cc parallel-twin with intercooled
Suzuki_Recursion
Type of grammar for describing formal languages
parsing, left recursion must be eliminated. Direct recursion, be that left or right, is important in context-free grammars, because there recursion is the only
Parsing_expression_grammar
Theory of the biological component of the language faculty
present in both human and non-human animals, the computational mechanism of recursion has evolved recently, and solely in humans. The presence of creole languages
Universal_grammar
Programming language family
storage management, dynamic typing, conditionals, higher-order functions, recursion, the self-hosting compiler, and the read–eval–print loop. The name LISP
Lisp_(programming_language)
Programming paradigm restricted to provably terminating programs
restricted form of recursion, which operates only upon 'reduced' forms of its arguments, such as Walther recursion, substructural recursion, or "strongly normalizing"
Total_functional_programming
Rewriting system and type of formal grammar
above to the earlier recursion, one gets: Axiom First recursion Second recursion Third recursion Fourth recursion Seventh recursion, scaled down ten times
L-system
Quickly growing function
stack reflects the recursion depth. As the reduction according to the rules {r4, r5, r7} involves a smaller maximum depth of recursion, this computation
Ackermann_function
Object-oriented programming system problem
blamed on open recursion (dynamic dispatch of methods on this), with the suggestion that invoking methods on this default to closed recursion (static dispatch
Fragile_base_class
American mathematician (1909–1994)
best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical
Stephen_Cole_Kleene
Sequence of program instructions invokable by other software
suspend while another nested execution of the same callable executes. Recursion is a useful means to simplify some complex algorithms and break down complex
Function (computer programming)
Function_(computer_programming)
Endless sequence of integers
previous elements in a straightforward way, they are often defined using recursion. Recamán's sequence was named after its inventor, Colombian mathematician
Recamán's_sequence
Island or lake that is itself within an island or lake
that lies inside a lake, or vice versa. For the purposes of defining recursion, small continental land masses such as Madagascar and New Zealand count
Recursive_islands_and_lakes
Technique for defining number-theoretic functions by recursion
course-of-values recursion is a technique for defining number-theoretic functions by recursion. In a definition of a function f by course-of-values recursion, the
Course-of-values_recursion
Malicious archive file designed to disrupt the program or system reading it
a maximum size for quadratic growth. Recursion bombs: In many anti-virus scanners, only a few layers of recursion are performed on archives to help prevent
Zip_bomb
Computer algorithm for evaluating compiler implementations
of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not. There are quite a few
Man_or_boy_test
General-purpose programming language
language, supporting structured programming, lexical variable scope, and recursion, with a static type system. It was designed to be compiled to provide
C_(programming_language)
Theoretical framework of management cybernetics
viable system. Society itself can be seen as a system of recursion. In this case, recursion refers to systems that are nested within other systems. (Axioms
Viable_system_model
Recursion without calling a function by name
In computer science, anonymous recursion is recursion which does not explicitly call a function by name. This can be done either explicitly, by using a
Anonymous_recursion
Type of algorithm in computer science
corecursion is a type of operation that is dual to (structural) recursion. Whereas recursion consumes a data structure by first handling the topmost layer
Corecursion
Function computable with bounded loops
composition h ∘ g 1 {\displaystyle h\circ g_{1}} is obtained. Primitive recursion operator ρ {\displaystyle \rho } : Given the k-ary function g ( x 1 ,
Primitive_recursive_function
Method of solving differential equations
coded using recursion. Since the function calls itself with smaller sized (coarser) parameters, the coarsest grid is where the recursion stops. In cases
Multigrid_method
Parsing technique
Frost, Hafiz, and Callaghan, which do accommodate ambiguity and left recursion in polynomial time and which generate polynomial-sized representations
Top-down_parsing
Alternate way to define a function in APL
new-lines, wherein ⍺ denotes the left argument and ⍵ the right, and ∇ denotes recursion (function self-reference). For example, the function PT tests whether
Direct_function
Method of comparing problems by transforming one into another in computability theory
Odifreddi, 1989. Classical Recursion Theory, North-Holland. ISBN 0-444-87295-7 P. Odifreddi, 1999. Classical Recursion Theory, Volume II, Elsevier.
Reduction (computability theory)
Reduction_(computability_theory)
Top-down parser utilizing recursion
left recursion. Any context-free grammar can be transformed into an equivalent grammar that has no left recursion, but removal of left recursion does
Recursive_descent_parser
Logical connective AND
problem Kolmogorov complexity Lambda calculus Primitive recursive function Recursion Recursive set Turing machine Type theory Related Abstract logic Algebraic
Logical_conjunction
Coding guidelines by Gerald J. Holzmann
goto statements, setjmp or longjmp constructs, or direct or indirect recursion. Give all loops a fixed upper bound. It must be trivially possible for
The Power of 10: Rules for Developing Safety-Critical Code
The_Power_of_10:_Rules_for_Developing_Safety-Critical_Code
Mathematical system
In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative
Second-order_arithmetic
One of several equivalent definitions of a computable function
U_{2}^{3})\right)} Fibonacci number McCarthy 91 function Recursion theory Recursion Recursion (computer science) "Recursive Functions". The Stanford Encyclopedia
General_recursive_function
Generalization of "n-th" to infinite cases
ordinals. This is known as transfinite recursion. Formally, a function F is defined by transfinite recursion on the ordinals if, for every ordinal α
Ordinal_number
Representation theory
}(1-p^{n}q^{m})^{c_{nm}}} for the elliptic modular function j. Peterson gave a recursion formula for the multiplicities mult(β) of the roots β of a symmetrizable
Weyl_character_formula
Mathematical function that can be computed by a program
and projection functions, and is closed under composition, primitive recursion, and the μ operator. Equivalently, computable functions can be formalized
Computable_function
Generalization of addition, multiplication, exponentiation, tetration, etc.
copies of }}a},\quad n\geq 2} It may also be defined according to the recursion rule part of the definition, as in Knuth's up-arrow version of the Ackermann
Hyperoperation
Proof method in mathematical logic
induction. Structural recursion is a recursion method bearing the same relationship to structural induction as ordinary recursion bears to ordinary mathematical
Structural_induction
Ethnic group in the Amazon Rainforest
that it has no relative clauses or grammatical recursion. Everett points out that there is recursion of ideas: that in a story, there may be subordinate
Pirahã_people
Divide and conquer sorting algorithm
Pages 10–16. Later, Hoare learned about ALGOL and its ability to do recursion, which enabled him to publish an improved version of the algorithm in
Quicksort
Branch of mathematical logic
The use of second-order arithmetic also allows many techniques from recursion theory to be employed; many results in reverse mathematics have corresponding
Reverse_mathematics
Algorithm for integer multiplication
products can be computed by recursive calls of the Karatsuba algorithm. The recursion can be applied until the numbers are so small that they can (or must)
Karatsuba_algorithm
Programming language
SuperPascal is an imperative, concurrent computing programming language developed by Per Brinch Hansen. It was designed as a publication language: a thinking
SuperPascal
Muran language
researchers, numerals and counting are based on recursion in the language, the absence of recursion in their language entails a lack of counting. That
Pirahã_language
use of recursion to extend the expressibility of the logic, and is commonly referred to as 'Hennessy-Milner Logic with recursion'. Recursion is enabled
Hennessy–Milner_logic
Study of circular causal processes
transdisciplinary study of circular causal processes such as feedback and recursion, where the outcomes of actions return as inputs for subsequent actions
Cybernetics
Computer science and recursion theory
In computer science and recursion theory the McCarthy formalism (1963) of computer scientist John McCarthy clarifies the notion of recursive functions
McCarthy_Formalism
Measure of unsolvability
on some Tn such that machines <i that halt on X do so <n−i steps (by recursion, this is uniformly computable from 0′). X is noncomputable since otherwise
Turing_degree
Thesis on the nature of computability
functions (with arbitrarily many arguments) that is closed under composition, recursion, and minimization, and includes zero, successor, and all projections.
Church–Turing_thesis
Integration of programming as part of running program
and recursion solutions, but timing had been a major issue. While the general form of a temporal recursion, being any asynchronous function recursion through
Live_coding
2.1), Microsoft SQL Server (starting with version 2005), Oracle (with recursion since 11g release 2), PostgreSQL (since 8.4), MariaDB (since 10.2), MySQL
Hierarchical and recursive queries in SQL
Hierarchical_and_recursive_queries_in_SQL
Algorithm for finding max graph matchings
graphs and directly addresses these challenges. It first introduces a new recursion-free Blossom algorithm. In the traditional algorithm, a blossom is contracted
Blossom_algorithm
1957 technique for modelling problems of decision making under uncertainty
forward recursion or backward recursion algorithms, as outlined below. Stochastic dynamic programs can be solved to optimality by using backward recursion or
Stochastic dynamic programming
Stochastic_dynamic_programming
Fractal composed of triangles
Sierpiński pyramid recursion (8 steps)
Sierpiński_triangle
Method in numerical analysis
_{1}(x)+a_{2}T_{2}(x)+\cdots +a_{n}T_{n}(x).} The coefficients in the recursion relation for the Chebyshev polynomials are α ( x ) = 2 x , β = − 1 , {\displaystyle
Clenshaw_algorithm
Tool for analyzing divide-and-conquer algorithms
p(input x of size n): if n < some constant k: Solve x directly without recursion else: Create a subproblems of x, each having size n/b Call procedure p
Master theorem (analysis of algorithms)
Master_theorem_(analysis_of_algorithms)
American logician (1933–2019)
2019) was an American logician whose most important contributions were in recursion theory. Named after him is Sacks forcing, a forcing notion based on perfect
Gerald_Sacks
Transmission of information
of meaning into more complex meaning structures. One view states that recursion sets human language apart from all non-human communicative systems. Another
Communication
Non-comparative lexicographical sorting algorithm
required by LSD. However, MSD sorts are more amenable to subdivision and recursion. Each bucket created by an MSD step can itself be radix sorted using the
Radix_sort
Sequence of operations for a task
Undecidable, p. 237ff. Kleene's definition of "general recursion" (known now as mu-recursion) was used by Church in his 1935 paper An Unsolvable Problem
Algorithm
Type of parser
But it fails to accept 'aaaa' {\displaystyle {\texttt {'aaaa'}}} . Left recursion happens when a grammar production refers to itself as its left-most element
Packrat_parser
Method using forcing to construct sets with desired properties in computability theory
\phi } will be true. Fitting, Melvin (1981). Fundamentals of generalized recursion theory. Studies in Logic and the Foundations of Mathematics. Vol. 105
Forcing_(computability)
Formal system in mathematical logic
such as products, coproducts or natural numbers (System T) or even full recursion (like PCF). In contrast, systems that introduce polymorphic types (like
Simply_typed_lambda_calculus
Functional programming language
Epigram is a functional programming language with dependent types, and the integrated development environment (IDE) usually packaged with the language
Epigram (programming language)
Epigram_(programming_language)
Mathematical function characterizing set membership
function. (See paragraph below about the use of the inverse in classical recursion theory.) Given a probability space ( Ω , F , P ) {\displaystyle \textstyle
Indicator_function
Family of higher-order functions
second argument, and the rest of the result is never demanded, then the recursion will stop (e.g., head == foldr (\a b->a) (error "empty list")). This allows
Fold_(higher-order_function)
Topics referred to by the same term
Look up recurring, recur, or recursion in Wiktionary, the free dictionary. Recurring means occurring repeatedly and can refer to several different things:
Recurring
Defining elements of a set in terms of other elements in the set
\end{aligned}}} This definition is valid for each natural number n, because the recursion eventually reaches the base case of 0. The definition may also be thought
Recursive_definition
RECURSION
RECURSION
RECURSION
RECURSION
Boy/Male
Arabic, Muslim
Glorious; Magnificent
Girl/Female
Arabic, Muslim
Dew; Generosity; Damp; Tender; Feminine of Nadi; Delicate
Girl/Female
Tamil
Bahugandha | பஹà¯à®•à®‚தா
One with lot of scent
Boy/Male
Indian, Punjabi, Sikh
Pure One
Boy/Male
Indian
King of Gold
Girl/Female
Indian
Boy/Male
American, British, English
Lives at the Elm Tree Moor
Surname or Lastname
English
English : unexplained. Compare Starnes.
Boy/Male
Indian
Successful, Turquoise, Gem stone
Boy/Male
British, English
From the Sandy Stream
RECURSION
RECURSION
RECURSION
RECURSION
RECURSION
n.
The act of recurring; return.